| Title:
|
Time-periodic solutions of a quasilinear beam equation via accelerated convergence methods (English) |
| Author:
|
Feireisl, Eduard |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
33 |
| Issue:
|
5 |
| Year:
|
1988 |
| Pages:
|
362-373 |
| Summary lang:
|
English |
| Summary lang:
|
Russian |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
The author investigates time-periodic solutions of the quasilinear beam equation with the help of accelerated convergence methods. Using the Newton iteration scheme, the problem is approximated by a sequence of linear equations solved via the Galerkin method. The derivatiove loss inherent to this kind of problems is compensated by taking advantage of smoothing operators. (English) |
| Keyword:
|
accelerated convergence methods |
| Keyword:
|
smoothing operators |
| Keyword:
|
time-periodic solutions |
| Keyword:
|
quasilinear beam equation |
| Keyword:
|
Newton method |
| Keyword:
|
Galerkin method |
| MSC:
|
35B10 |
| MSC:
|
35L70 |
| MSC:
|
35L75 |
| MSC:
|
58C15 |
| MSC:
|
65N35 |
| MSC:
|
65Z05 |
| MSC:
|
73K05 |
| MSC:
|
74K10 |
| idZBL:
|
Zbl 0665.65090 |
| idMR:
|
MR0961314 |
| DOI:
|
10.21136/AM.1988.104317 |
| . |
| Date available:
|
2008-05-20T18:35:15Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104317 |
| . |
| Reference:
|
[1] L. Hörmander: On the Nash-Moser implicit function theorem.Annal. Acad. Sci. Fennicae, Ser. A, 10 (1985) pp. 255-259. MR 0802486 |
| Reference:
|
[2] S. Klainerman: Global existence for nonlinear wave equations.Comm. Pure Appl. Math. 33 (1980), pp. 43-101. Zbl 0405.35056, MR 0544044, 10.1002/cpa.3160330104 |
| Reference:
|
[3] P. Krejčí: Hard implicit function theorem and small periodic solutions to partial differential equations.Comment. Math. Univ. Carolinae 25 (1984), pp. 519-536. MR 0775567 |
| Reference:
|
[4] A. Matsumura: Global existence and asymptotics of the solutions of the second order quasilinear hyperbolic equations with the first order dissipation.Publ. Res. Inst. Math. Soc. 13 (1977), pp. 349-379. Zbl 0371.35030, MR 0470507, 10.2977/prims/1195189813 |
| Reference:
|
[5] J. Moser: A rapidly-convergent iteration method and non-linear differential equations.Ann. Scuola Norm. Sup. Pisa 20-3 (1966), pp. 265-315, 499-535. Zbl 0174.47801 |
| Reference:
|
[6] H. Petzeltová: Application of Moser's method to a certain type of evolution equations.Czechoslovak Math. J. 33 (1983), pp. 427-434. Zbl 0547.35081, MR 0718925 |
| Reference:
|
[7] H. Petzeltová M. Štědrý: Time-periodic solutions of telegraph equations in n spatial variables.Časopis pěst. mat. 109 (1984), pp. 60-73. MR 0741209 |
| Reference:
|
[8] M. Štědrý: Periodic solutions of nonlinear equations of a beam with damping.Czech. Thesis, Math. Inst. Czechoslovak Acad. Sci., Prague 1973. |
| Reference:
|
[9] O. Vejvoda, al.: Partial differential equations - time periodic solutions.Sijthoff Noordhoff 1981. |
| . |
